{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "code",
      "source": [
        "!pip install qutip matplotlib numpy\n",
        "\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from qutip import *\n",
        "\n",
        "print(\"🔬 Advanced QuTip Tutorial: Quantum Dynamics & Entanglement\")\n",
        "print(\"=\" * 60)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "TGX4GilNQwww",
        "outputId": "2ecdb4c8-30a5-459c-e7ca-56f082c43b3d"
      },
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Requirement already satisfied: qutip in /usr/local/lib/python3.11/dist-packages (5.2.0)\n",
            "Requirement already satisfied: matplotlib in /usr/local/lib/python3.11/dist-packages (3.10.0)\n",
            "Requirement already satisfied: numpy in /usr/local/lib/python3.11/dist-packages (2.0.2)\n",
            "Requirement already satisfied: scipy>=1.9 in /usr/local/lib/python3.11/dist-packages (from qutip) (1.15.3)\n",
            "Requirement already satisfied: packaging in /usr/local/lib/python3.11/dist-packages (from qutip) (24.2)\n",
            "Requirement already satisfied: contourpy>=1.0.1 in /usr/local/lib/python3.11/dist-packages (from matplotlib) (1.3.2)\n",
            "Requirement already satisfied: cycler>=0.10 in /usr/local/lib/python3.11/dist-packages (from matplotlib) (0.12.1)\n",
            "Requirement already satisfied: fonttools>=4.22.0 in /usr/local/lib/python3.11/dist-packages (from matplotlib) (4.58.4)\n",
            "Requirement already satisfied: kiwisolver>=1.3.1 in /usr/local/lib/python3.11/dist-packages (from matplotlib) (1.4.8)\n",
            "Requirement already satisfied: pillow>=8 in /usr/local/lib/python3.11/dist-packages (from matplotlib) (11.2.1)\n",
            "Requirement already satisfied: pyparsing>=2.3.1 in /usr/local/lib/python3.11/dist-packages (from matplotlib) (3.2.3)\n",
            "Requirement already satisfied: python-dateutil>=2.7 in /usr/local/lib/python3.11/dist-packages (from matplotlib) (2.9.0.post0)\n",
            "Requirement already satisfied: six>=1.5 in /usr/local/lib/python3.11/dist-packages (from python-dateutil>=2.7->matplotlib) (1.17.0)\n",
            "🔬 Advanced QuTip Tutorial: Quantum Dynamics & Entanglement\n",
            "============================================================\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "print(\"\\n1. Creating Quantum States\")\n",
        "ground = basis(2, 0)\n",
        "excited = basis(2, 1)\n",
        "plus = (ground + excited).unit()\n",
        "minus = (ground - excited).unit()\n",
        "\n",
        "print(f\"Ground state |0⟩: {ground.dag()}\")\n",
        "print(f\"Superposition |+⟩: {plus.dag()}\")\n",
        "\n",
        "bell_phi_plus = (tensor(ground, ground) + tensor(excited, excited)).unit()\n",
        "bell_psi_minus = (tensor(ground, excited) - tensor(excited, ground)).unit()\n",
        "\n",
        "print(f\"\\nBell state |Φ+⟩ = (|00⟩ + |11⟩)/√2\")\n",
        "rho_bell = bell_phi_plus * bell_phi_plus.dag()\n",
        "print(f\"Entanglement measure: {concurrence(rho_bell):.3f}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "IU2H9bXmQy5-",
        "outputId": "2864e585-cab3-45d9-c518-8410ec63d703"
      },
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "1. Creating Quantum States\n",
            "Ground state |0⟩: Quantum object: dims=[[1], [2]], shape=(1, 2), type='bra', dtype=Dense\n",
            "Qobj data =\n",
            "[[1. 0.]]\n",
            "Superposition |+⟩: Quantum object: dims=[[1], [2]], shape=(1, 2), type='bra', dtype=Dense\n",
            "Qobj data =\n",
            "[[0.70710678 0.70710678]]\n",
            "\n",
            "Bell state |Φ+⟩ = (|00⟩ + |11⟩)/√2\n",
            "Entanglement measure: 1.000\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "print(\"\\n2. Quantum Gates and Operations\")\n",
        "sx, sy, sz = sigmax(), sigmay(), sigmaz()\n",
        "print(f\"Pauli-X matrix:\\n{sx}\")\n",
        "\n",
        "hadamard = (sx + sz) / np.sqrt(2)\n",
        "cnot = tensor(fock_dm(2, 0), qeye(2)) + tensor(fock_dm(2, 1), sx)\n",
        "\n",
        "h_ground = hadamard * ground\n",
        "print(f\"\\nH|0⟩ = {h_ground.dag()}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "qnuEcD6JQ-So",
        "outputId": "582e3713-af85-4466-8178-fdbbc5e6ce59"
      },
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "2. Quantum Gates and Operations\n",
            "Pauli-X matrix:\n",
            "Quantum object: dims=[[2], [2]], shape=(2, 2), type='oper', dtype=CSR, isherm=True\n",
            "Qobj data =\n",
            "[[0. 1.]\n",
            " [1. 0.]]\n",
            "\n",
            "H|0⟩ = Quantum object: dims=[[1], [2]], shape=(1, 2), type='bra', dtype=Dense\n",
            "Qobj data =\n",
            "[[0.70710678 0.70710678]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "print(\"\\n3. Quantum Dynamics: Rabi Oscillations\")\n",
        "omega_0 = 1.0\n",
        "omega_r = 0.5\n",
        "\n",
        "H = 0.5 * omega_0 * sz + 0.5 * omega_r * sx\n",
        "\n",
        "t_list = np.linspace(0, 4*np.pi/omega_r, 100)\n",
        "psi0 = ground\n",
        "result = mesolve(H, psi0, t_list, [], [])\n",
        "\n",
        "excited_pop = [expect(fock_dm(2, 1), state) for state in result.states]\n",
        "\n",
        "plt.figure(figsize=(12, 4))\n",
        "plt.subplot(1, 2, 1)\n",
        "plt.plot(t_list, excited_pop, 'b-', linewidth=2)\n",
        "plt.xlabel('Time (ℏ/ω)')\n",
        "plt.ylabel('Excited State Population')\n",
        "plt.title('Rabi Oscillations')\n",
        "plt.grid(True, alpha=0.3)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 447
        },
        "id": "oUtVPUW0RCXC",
        "outputId": "bb1fc859-26b9-4f4e-86aa-08e49849eb6e"
      },
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "3. Quantum Dynamics: Rabi Oscillations\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1200x400 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "print(\"\\n4. Quantum Harmonic Oscillator\")\n",
        "N = 20\n",
        "a = destroy(N)\n",
        "H_ho = a.dag() * a + 0.5\n",
        "\n",
        "alpha = 2.0\n",
        "psi0_coh = coherent(N, alpha)\n",
        "\n",
        "t_list_ho = np.linspace(0, 2*np.pi, 50)\n",
        "result_ho = mesolve(H_ho, psi0_coh, t_list_ho, [], [])\n",
        "\n",
        "x_op = (a + a.dag()) / np.sqrt(2)\n",
        "p_op = 1j * (a.dag() - a) / np.sqrt(2)\n",
        "\n",
        "x_expect = [expect(x_op, state) for state in result_ho.states]\n",
        "p_expect = [expect(p_op, state) for state in result_ho.states]\n",
        "\n",
        "plt.subplot(1, 2, 2)\n",
        "plt.plot(x_expect, p_expect, 'r-', linewidth=2)\n",
        "plt.plot(x_expect[0], p_expect[0], 'go', markersize=8, label='Start')\n",
        "plt.plot(x_expect[-1], p_expect[-1], 'ro', markersize=8, label='End')\n",
        "plt.xlabel('⟨x⟩')\n",
        "plt.ylabel('⟨p⟩')\n",
        "plt.title('Coherent State Phase Space')\n",
        "plt.legend()\n",
        "plt.grid(True, alpha=0.3)\n",
        "plt.axis('equal')\n",
        "\n",
        "plt.tight_layout()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 524
        },
        "id": "7f1-gxLDRJ9D",
        "outputId": "eabf8cfb-a11e-47ff-acbd-01d3f51c9974"
      },
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "4. Quantum Harmonic Oscillator\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "print(\"\\n5. Quantum Decoherence and Open Systems\")\n",
        "gamma = 0.2\n",
        "n_th = 0.1\n",
        "\n",
        "c_ops = [np.sqrt(gamma * (1 + n_th)) * a, np.sqrt(gamma * n_th) * a.dag()]\n",
        "\n",
        "psi0_sq = squeeze(N, 0.5) * basis(N, 0)\n",
        "\n",
        "t_list_damp = np.linspace(0, 10, 100)\n",
        "result_damp = mesolve(H_ho, psi0_sq, t_list_damp, c_ops, [])\n",
        "\n",
        "n_expect = [expect(a.dag() * a, state) for state in result_damp.states]\n",
        "\n",
        "plt.figure(figsize=(10, 4))\n",
        "plt.subplot(1, 2, 1)\n",
        "plt.plot(t_list_damp, n_expect, 'g-', linewidth=2)\n",
        "plt.xlabel('Time')\n",
        "plt.ylabel('⟨n⟩')\n",
        "plt.title('Photon Number Decay')\n",
        "plt.grid(True, alpha=0.3)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 447
        },
        "id": "j3CkwsB7RVA0",
        "outputId": "e79ac3dc-71a5-49ac-b8c0-e9b26be96d78"
      },
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "5. Quantum Decoherence and Open Systems\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x400 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "print(\"\\n6. Wigner Function Visualization\")\n",
        "final_state = result_damp.states[-1]\n",
        "xvec = np.linspace(-4, 4, 50)\n",
        "W_final = wigner(final_state, xvec, xvec)\n",
        "\n",
        "plt.subplot(1, 2, 2)\n",
        "plt.contourf(xvec, xvec, W_final, 20, cmap='RdBu')\n",
        "plt.colorbar(label='W(x,p)')\n",
        "plt.xlabel('x')\n",
        "plt.ylabel('p')\n",
        "plt.title('Wigner Function (Final State)')\n",
        "\n",
        "plt.tight_layout()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 524
        },
        "id": "UpEWy508Rclb",
        "outputId": "85730870-2181-4606-dc69-c0eebc1f1eb4"
      },
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "6. Wigner Function Visualization\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "print(\"\\n7. Entanglement Dynamics\")\n",
        "omega1, omega2 = 1.0, 1.1\n",
        "g = 0.1\n",
        "\n",
        "H_coupled = (omega1/2 * tensor(sz, qeye(2)) +\n",
        "             omega2/2 * tensor(qeye(2), sz) +\n",
        "             g * tensor(sx, sx))\n",
        "\n",
        "psi0_prod = tensor(plus, ground)\n",
        "\n",
        "t_list_ent = np.linspace(0, 20, 200)\n",
        "result_ent = mesolve(H_coupled, psi0_prod, t_list_ent, [], [])\n",
        "\n",
        "entanglement = [concurrence(state * state.dag()) for state in result_ent.states]\n",
        "\n",
        "plt.figure(figsize=(8, 5))\n",
        "plt.plot(t_list_ent, entanglement, 'purple', linewidth=2)\n",
        "plt.xlabel('Time')\n",
        "plt.ylabel('Concurrence')\n",
        "plt.title('Entanglement Generation in Coupled Qubits')\n",
        "plt.grid(True, alpha=0.3)\n",
        "plt.ylim(0, 1)\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 524
        },
        "id": "OdWaBpm6RenF",
        "outputId": "c7bc5379-6c61-4322-fc63-d4109ef5d9a2"
      },
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "7. Entanglement Dynamics\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 800x500 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 11,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "X0JqSWyIOoYT",
        "outputId": "e3fc29a7-4657-4381-f35b-1946b6b0ffee"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "8. Summary of Advanced Features Demonstrated:\n",
            "✓ Quantum state preparation and manipulation\n",
            "✓ Time evolution with mesolve()\n",
            "✓ Rabi oscillations in two-level systems\n",
            "✓ Coherent states and harmonic oscillators\n",
            "✓ Open quantum systems with decoherence\n",
            "✓ Wigner function visualization\n",
            "✓ Entanglement quantification and dynamics\n",
            "\n",
            "🎯 Tutorial complete! Explored 200 time steps\n",
            "Try modifying parameters to explore different quantum phenomena!\n",
            "\n",
            "💡 Advanced Exercises:\n",
            "1. Implement quantum error correction codes\n",
            "2. Simulate quantum algorithms (Grover, Shor)\n",
            "3. Explore cavity QED with Jaynes-Cummings model\n",
            "4. Study quantum phase transitions\n",
            "5. Implement quantum feedback control\n"
          ]
        }
      ],
      "source": [
        "print(\"\\n8. Summary of Advanced Features Demonstrated:\")\n",
        "print(\"✓ Quantum state preparation and manipulation\")\n",
        "print(\"✓ Time evolution with mesolve()\")\n",
        "print(\"✓ Rabi oscillations in two-level systems\")\n",
        "print(\"✓ Coherent states and harmonic oscillators\")\n",
        "print(\"✓ Open quantum systems with decoherence\")\n",
        "print(\"✓ Wigner function visualization\")\n",
        "print(\"✓ Entanglement quantification and dynamics\")\n",
        "\n",
        "print(f\"\\n🎯 Tutorial complete! Explored {len(t_list_ent)} time steps\")\n",
        "print(\"Try modifying parameters to explore different quantum phenomena!\")\n",
        "\n",
        "print(\"\\n💡 Advanced Exercises:\")\n",
        "print(\"1. Implement quantum error correction codes\")\n",
        "print(\"2. Simulate quantum algorithms (Grover, Shor)\")\n",
        "print(\"3. Explore cavity QED with Jaynes-Cummings model\")\n",
        "print(\"4. Study quantum phase transitions\")\n",
        "print(\"5. Implement quantum feedback control\")"
      ]
    }
  ]
}